Maxwell–Boltzmann distribution

About: Maxwell–Boltzmann distribution is a research topic. Over the lifetime, 853 publications have been published within this topic receiving 16952 citations. The topic is also known as: Maxwell distribution.

On the Resistance Experienced by Spheres in their Motion through Gases

Abstract: Kinetic theory of the resistance to a sphere moving through a gas.— (1) Droplets small in comparison with the mean free path. The high degree of accuracy achieved in the experimental determination of the law of motions of droplets through gases, makes a careful theoretical examination of the problem desirable. Assuming the usual Maxwellian distribution of velocities in the gas, the force exerted by the impinging molecules is found to be M where M=(4π/3) Nma2cmV, N, m, a, and cm being the number per unit volume, mass, radius, and mean speed of the molecules and V the speed of the droplet. The force exerted by the molecules leaving the surface depends on how they leave. (1) For uniform evaporation from the whole surface, the force is -M; (2) for specular reflection of all the impinging molecules, -M; (3) for diffuse reflection with unchanged distribution of velocities, -(13/9)M; (4) for diffuse reflection with the Maxwell distribution corresponding to the effective temperature of the part of the surface they come from, -(1+9π/64)M, for a non-conducting droplet (4a), and -(1+π/8)M, for a perfectly conducting droplet (4b). Cases (1) and (2) can not be distinguished experimentally, but (2) is more probable physically. The experimental values agree with 1/10 specular reflection, case (2), and 9/10 diffuse reflection, case (4a) or (4b). For large values of l/a, the droplet behaves like a perfect conductor, case (4b). (2) Comparatively large spheres. The distribution of velocities is no longer Maxwellian because of the hydrodynamic stresses which can not now be neglected. The new law is derived (Eq. 47). The conditions at the surface of the sphere are discussed and it is shown that the diffusely reflected molecules have a Maxwellian distribution corresponding to the temperature and density of the gas, just as though they were reflected with conservation of velocity (specularly). The assumptions of Bassett are theoretically justified and a complete confirmation is obtained for the correction factor for Stokes' law [1+0.7004 (2/s-1) (l/a)] on which Millikan's conclusions are based, especially as to the percentage of specular reflection. (3) Rotating spheres are also considered in an appendix, and the values of the resistance are derived for various cases.

Electron Radiative Transitions in a Coulomb Field

Abstract: Free-free, bound-free, and bound-bound Gaunt factors and oscillator strengths were computed for electrons in a pure Coulomb potential. Numerical results are presented for a wide range of electron and photon energies. In addition, for the free-free case, average Gaunt factors and the rate of bremsstrahlung production were obtained as functions of temperature for a Boltzmann distribution of electron energies.

Monte Carlo Calculations of Nuclear Evaporation Processes. III. Applications to Low-Energy Reactions

Abstract: Monte Carlo calculations of nuclear reactions in the low-energy (E < 50 Mev) region are described. The calculations are based on the nuclear evaporation model of Weisskopf. Continuum theory was used for the calculation of inverse reaction cross sections. In the calculation of the level densities of excited nuclei, pairing and shell energy corrections were used in terms of charactertstic level displacements. The accurate equation rather than the approximate Maxwell distribution was used for the selection of the kinetic energy of the evaporated particle. Experimentally determined Q-values for the various reactions were used. The calculations are compared with experimental measurements for about 60 excitation functions of nuclear reactions in the mass range Cr/sup 50/-Se/sup 74/. Cameron's values for pairing energies were used at the outset; but a new set of pairing and shell energy correction values, which leads to substuntially improved agreement with the experimental curves, Is presented. The procedure which was used to arrive at this set is described and several features of the set are discussed. The need for a further downward correction of the level density of symmetrical (A = 2Z) nuclei is indicated. Computed excitation functions are shown for all the reactions studied as well asmore » for several reactions for which experimental data are not yet available. Further experiments on reaction cross sections are suggested which would allow a unique deterntination of the pairing and shell energy corrections of level densities for any value of Z and N in the region under discussion. The existence of a unique set of these correction terms would provide strong evidence for the validity of evaporation theory for the reactions considered. (auth)« less